how do I animate a vesicle fusing to a cell membrane?
Could you add some reference images of the effect you are trying to achieve? It is not clear what you want to do.

Would it be something similar to what's illustrated bellow? You can easily create merging/blending soft shapes with meta geometries.

Just create two meta ball objects withShift+A > Meta Ball, scale them down accordingly, then adjust the properties as desired as the Threshold and Resolution. 
Move them around and their geometry should just fuse together naturally.